As is known, matter in a fluid, liquid or gaseous, state is vitally important to the biosphere as well as to human activities. For instance, for societies whose economy is based primarily on agriculture and/or cattle breeding, an abundance of water may be a primary consideration among the factors that ensure development and prosperity. On the other hand, in industrial societies, a number of other fluids, besides water, are critical to the fostering of development.
Of major concern are the problems of tracing such fluids, processing and dispensing them to millions of users. Closely related to such problems is also the manner in which the mass, volume and flow rate of the fluids are measured. A range of different systems for measuring the flow rate and velocity of a stream of fluid have been produced through the years. But the systems currently available on the market have evolved in view of industrial applications, and their cost is often high enough to forbid their adoption for domestic applications on any large scale.
The flow measuring systems proposed by the state of the art are based on different physical principles, and vary according to the kind of fluid to be measured for velocity. In all cases, the measuring systems currently available on the market are relatively expensive, and in general, have shapes and dimensions that make them impractical to merchandise in large volumes for domestic applications.
Briefly reviewed herein below are some of the conventional techniques employed for measuring the velocity or the flow rate of fluids.
1) Pitot Tube.
A Pitot tube allows the velocity head v of a fluid flow of known direction to be measured by taking pressure measurements at two points in a conduit of suitable shape.
The velocity head v of the flow is obtained from the following relationship: ##EQU1## where: V is the flow velocity, [m/s];
.rho. is the mass density of the fluid, [kg/m.sup.3 ]; PA1 P.sub.stag is the stagnation pressure, [Pa]; and PA1 P.sub.stat is the static pressure, [Pa]. PA1 a misalignment between the velocity vector and the tube axis (whereby the static pressure measurement can be biased by pressure components due to velocity); PA1 a diameter dimension of the tube altering the normal fluid flow; the stream lines near the tube surface are indeed longer than those in the undisturbed region, resulting in increased velocity and, hence, decreased static pressure; PA1 the influence of the supporting tube on the stagnation pressure; and PA1 viscosity exerting an additional force on the stagnation cavity, so that a higher stagnation pressure is produced than anticipated. PA1 .rho. is the mass density of the fluid, [kg/m.sup.3 ]; and PA1 p.sub.1 and p.sub.2 are the static pressures as measured at points in the conduit having the cross-sectional areas A.sub.1f and A.sub.2f, respectively, [Pa]. PA1 A is the conduit cross-section. [m.sup.2 ]; PA1 .rho. is the mass density of the fluid, [kg/m.sup.3 ]; and PA1 v is the velocity of the fluid, [m/s]. PA1 dU is the energy variation internally of the probe per unit time, [W]; PA1 Eg is the thermal energy generated within the probe per unit time, [W]; PA1 Es is the thermal energy exchanged between the hot wire and the fluid per unit time. [W]. PA1 .rho. is the mass density of the probe, [kg/m.sup.3 ]; PA1 C is the thermal capacity of the probe, [m.sup.2 /s.sup.2 .degree. K.]; PA1 V is the volume of the probe, [m.sup.3 ]; PA1 A is the surface area of the probe, [m.sup.2 ]; PA1 R is the electric resistance of the probe, PA1 h is a heat exchange coefficient (forced convection coefficient), [kg/s.sup.3 .degree. K.]; PA1 T.sub.s is the probe temperature, [.degree. K.]; PA1 T.sub.f is the fluid temperature, [.degree. K.].
Therefore, once the density P of the fluid and the pressure differential between a stagnation pressure P.sub.stag and a static pressure P.sub.stat are known, the velocity v can be calculated. However, the measurement of the pressure differential is often affected by various sources of errors. In particular, the static pressure is difficult to measure accurately for the following reasons:
2) Laser-Doppler Speed Meter.
This device employs a laser light beam focused onto a point where the flow velocity is to be measured, and a photodetector to detect the diffused light from suspended foreign particles to be found naturally in unstrained fluids. The velocity of the particles, assumed to be the same as that of the fluid, causes a frequency variation in the diffused light which is tied to the fluid's own velocity. The flow velocity can be obtained by measuring this variation.
Major advantages of this device are that no physical objects need be introduced into the flow; accordingly, the fluid's own motion will be unperturbed; a fairly high frequency response can be obtained; and the volume required for carrying out the measurement can be fairly small.
On the other hand, the device also has disadvantages, as follows: transparent channels must be used; tracing particles must be provided within the fluid, unless they occur naturally in the fluid; and the equipment cost and complexity are considerable.
3) Restriction-Flow Flowmeter.
The most widely accepted principle used in the design of flow meters of this type is that of creating a restriction of predetermined cross-sectional area within the tube wherethrough the fluid is to run. This restriction causes a pressure drop which is dependent on the flow velocity. From a measurement of this pressure drop--to be taken on a suitable differential pressure pickup, for example--the flow rate q and flow velocity can be arrived at, according to the following relation: ##EQU2## where: A.sub.1f and A.sub.2f are the areas where the pressures p.sub.1 and p.sub.2 are respectively measured, [m.sup.2 ];
The advantages of these devices reside in their simple construction and low cost.
For practical use, the above relation should include correction factors. For example, A.sub.1f and A.sub.2f would not be the true areas corresponding to the diameters of the tube and the restriction, respectively, but rather the actual cross-sectional areas of the fluid flow. In real situations, effects due to friction are also present which lead to a loss of pressure head and errors in the pressure drop readings.
As follows from the above relation, a variation in the pressure differential by a ratio of 10:1 corresponds to a variation in the flow velocity by a ratio of 3:1. Since the meters used for measuring pressure differentials are wholly inaccurate at less than 10 percent of their full-scale value, this non-linearity, which is typical of all restriction meters, limits the flow measuring to within a range where the ratio of the maximum and minimum measurable values is 3:1.
4) Float-Type Flowmeter.
This is a useful instrument widely accepted for small and very small flow rates, where most of the other devices would be ineffective. It comprises a slightly conical tube containing a small ball or body of revolution, called the float although it would sink in the fluid being measured.
The tube is mounted vertically with its large base facing upwards. The fluid is admitted from underneath and lifts up the float until the free area between the float and the tube becomes such as to exactly meter the rate of flow to be measured across it, at a predetermined pressure drop almost entirely dependent on the ratio of the float weight (neglecting buoyancy) to the maximum cross-sectional area of the float. The height reached by the float is read directly on a scale, where the tube is transparent, or is measured by means of linkages or magnetic pickups where the tube is made of metal. This measuring step is illustrated by the schematic of accompanying FIG. 1.
Since the free area is, as a first approximation, proportional to the height attained by the float, and flow rate itself is proportional to the free area, the relation between flow rate and float lift is near-linear.
5) Rotor Counter.
The sensing element of this type of meter is an axial vane rotor driven rotatively by the fluid to be measured. The rotor flow-rate meter is extensively employed with fluids which have inherent lubricanting properties, such as hydrocarbons, so that frictional losses from the rotary gearing can be kept low.
The rotor bearings are here the most critical components, and require periodical replacement. The rotation is almost invariably measured by means of an inductive or capacitive type of proximity sensor which generates an electric pulse each time that a vane moves past a detection point. Good linearity and repeatability are advantages of this device. Major disadvantages are a high cost, mechanical fragility, and extensive maintenance requirements.
6) Measuring-Chamber Displacement Counter.
This is strictly a displacement meter. A volume of fluid, called the cyclic volume, is caused to flow at each cycle from inlet to outlet through constant volume moving chambers, or chambers which are alternately filled and emptied.
The fluid motion therethrough drives an output shaft rotatively. The power required for driving the mechanical members is sometimes provided by the fluid itself. The constructional and functional problems posed by these meters are those of tightness and wear. Accuracy is, in fact, affected therein by dimensional variations and fluid leakages that change with pressure and viscosity. In addition, the manufacturing cost of such meters is quite high.
7) Whirlpool Meter.
This device operates on the principle of detecting oscillatory phenomena artfully induced in the fluid. It comprises a barrel section accommodating a crosswise-laid body (C) which is shaped to produce in its wake a series of eddies which separate periodically and alternately to one side and the other. The pitch or distance between two successive eddies is, for a given size of the barrel, proportional to the mean velocity and flow rate of the fluid. The output signal can be produced from a shaped body caused to oscillate by the eddying action. The amplitude of the oscillation provides a measure of the flow velocity. Since the measurable flow rate is tied to the occurrence of eddies and the minimum detectable amplitude of the signal, the read range of such meters is rather narrow.
8) Drag Flowmeter.
The principle used by this meter is that of measuring the drag Fd of a body immersed in the fluid, as shown schematically in FIG. 2. This drag, to be measured by means of strain gage resistors suitably mounted to the stem that holds the submerged body, is tied to the flow velocity by the following relation: ##EQU3## where: C.sub.d is the drag coefficient (non-dimensional);
9) Electromagnetic Flowmeter.
This meter principle is based on Faradays law, whereby between the ends of conductor of length dl in motion at a speed v inside a magnetic field with induction B, an electromotive force is developed as given by: ##EQU4##
This law applies equally to conductors in the solid, liquid and gaseous state. Accordingly, if a magnetic field is created in a transverse direction along a pipe section wherethrough the fluid is being assed, the affected fluid will become the site of an electric field. A difference of potential is measured, between two electrodes placed within the field along an orthogonal diameter to the field, which is related to the flow velocity and flow rate.
In practical situations, the magnetic field has a limited extent, so that no voltage is induced in parts outside it; such parts will rather act as a short circuit reducing the voltage drop. This effect can be attenuated by increasing the extent of the magnetic field; for example, a length of three times the tube diameter is adequate. These meters can also be operated with slightly conductive liquids.
10) Ultrasonic Flowmeter.
This meter is characterized by excellent repeatability and linearity, as well as by its capability to measure flows in either directions and, within limits, even pulsating flow rates. In addition, some of these meters can take the measurement from outside the conduit, out of contact with the fluid; in no way do they significantly restrict the flow cross-section. They operate on either of at least two principles.
A first principle is based on Doppler's Effect. An emitter of ultrasound radiates ultrasonic waves at a given frequency f through a fluid containing tiny particles or bubbles suspended in a parallel direction to the flow direction. These particles being in motion, they will reflect part of the sound wave at a slightly lower frequency, when detected by a fixed receiver. Calling "a" the speed of sound through the fluid, and "v" the mean velocity of the reflective particles (v&lt;&lt;a), the frequency abatement of the reflected wave is: EQU .DELTA.f/f=2 v/a
A major drawback of this method is the dependence of the output signal on the speed of sound through the medium, and therefore on the nature and physical state of the liquid.
The second principle is illustrated schematically in FIG. 3, and is based on that the speed of the ultrasonic wave is added vectorially to that of the fluid medium through which it propagates. Shown in FIG. 3 are two pairs of transmitters T1, T2 and receivers R1, R2. The signal emitted from the first transmitter T1 will propagate to the receiver R1 at an absolute speed (a+v), and the signal from the second transmitter T2 at an absolute speed (a-v). Thus, the fluid velocity can be obtained by measuring the distance between the transmitters and the receivers and the difference between the propagation times of the ultrasonic signal in either directions. It can be shown that the output signal is unrelated to the speed of sound through the medium.
11) Heated Probe (Hot-Wire) Anemometer.
This anemometer operates on the principle of subtracting heat from thin wires by forced convection.
Illustrative of the type is the hot-wire anemometer, which comprises a platinum or tungsten wire having a diameter in the 5 to 50 .mu.m range and length of a few millimeters, its ends being soldered to two parallel needles. FIG. 4 shows schematically an example of this device.
A current I is flowed through the wire, whose resistance R is dependent on temperature. A power p=RI.sup.2 is produced by Joule's Effect, and the wire is heated. The wire is then swept orthogonally by a fluid stream having a velocity v and a set of different parameters. The thermal energy balance for the probe is given by: EQU dU=Eg-Es
where:
Substituting the probe own quantities for the terms, then: EQU .rho.CVdT.sub.s /dt=RI.sup.2 -hA (T.sub.s -T.sub.f)
where:
In steady conditions (dT.sub.s /dt=0), the thermal power delivered to the probe and that removed from it equal each other, so that: EQU RI.sup.2 -hA(T.sub.s -T.sub.f)
The heat exchange coefficient h is a function of a set of parameters of the fluid, including viscosity, conductivity, thermal capacity, velocity v, temperature T.sub.f, and of the surface thermal conductance of the probe. However, for a field of temperature differentials (T.sub.s -T.sub.f) within a given range and velocities between a few decimeters per second (below which, natural convection would prevail) and a few decameters per second, the parameter may be approximated as follows: ##EQU5## with the terms a and b being constant within the above range. Thus: ##EQU6##
With the current held constant, the velocity V of the fluid can be obtained from a voltage measurement across the heated probe, since all the terms of the equation are known, excepting v.
Unfortunately, this meter requires frequent re-calibration, even at intervals of a few hours, because the exposed wire is readily contaminated. For improved repeatability, screened wire or coated probes are used, wherein the wire is covered with a thin layer of quartz. These will obviously be sluggish in picking up viscosity, conductivity and thermal capacity variations of the fluid, since the heat exchange coefficient "h" is dependent on these quantities.